2024/01/08 by Taekyun Kim, Kim, Taekyun, Dae San Kim +1
Mathematics · #11B73 #11B83 #Analytic Number Theory Research #FOS: Mathematics #Geometry and complex manifolds #Mathematical functions and polynomials #Number Theory (math.NT) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2401.03986
openalex publication_date 2024/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the derangement polynomials, the derangement polynomials of type 2 and the r-derangement numbers, namely the probabilistic derangement polynomials associated with Y, the probabilistic derangement polynomials of type 2 associated with Y and the probabilistic r-derangement numbers associated Y, respectively. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials and numbers. In addition, we consider the special case that Y is the gamma random variable with parameters α,\beta > 0.